Abstract

We study the computational challenge faced by a intermediary who attempts to profit from trade with a small number of buyers and sellers of some item. In the version of the problem that we study, the number of buyers and sellers is constant, but their joint distribution of the item’s value may be complicated. We consider discretized distributions, where the complexity parameter is the support size, or number of different prices that may occur. We show that maximizing the expected revenue is computationally tractable (via an LP) if we are allowed to use randomized mechanisms. For the deterministic case, we show how an optimal mechanism can be efficiently computed for the one-seller/one-buyer case, but give a contrasting NP-completeness result for the one-seller/two-buyer case.